Intuitionistic Fuzzy Fixed Point Theory: Relation-Theoretic Approaches and Applications

Abstract

This paper explores the concept of intuitionistic fuzzy R-φ- contractive mappings and establishes key results regarding the existence and uniqueness of fixed points in non-Archimedean intuitionistic fuzzy metric spaces. To illustrate the applicability of these findings, several examples are provided. Additionally, the main results are utilized to demonstrate the existence and uniqueness of solutions for Caputo fractional differential equations within the framework of intuitionistic fuzzy metric spaces.